Offsprings of a point vortex

Offsprings of a point vortex

The distribution engendered by successive splitting of one point vortex are considered. The process of splitting a vortex in three using a reverse three-point vortex collapse course is analysed in great details and shown to be dissipative. A simple process of successive splitting is then defined and the resulting vorticity distribution and vortex populations are analysed. PACS. 0 5.20.-y, 05.45...

Convergence of the Point Vortex Methodfor 2 - D Vortex

We give an elementary proof of the convergence of the point vor-tex method (PVM) to a classical weak solution for the two-dimensional incom-pressible Euler equations with initial vorticity being a nite Radon measure of distinguished sign and the initial velocity of locally bounded energy. This includes the important example of vortex sheets, which exhibits the classical Kelvin-Helmholtz instabi...

A study of singularity formation in a vortex sheet by the point-vortex approximation

The initial-value problem for perturbations of a flat, constant-strength vortex sheet is linearly ill posed in the sense of Hadamard, owing to Kelvin-Helmholtz instability. Previous numerical studies of this problem have experienced difficulty in converging when the mesh was refined. The present work examines Rosenhead’s point-vortex approximation and seeks to understand better the source of th...

The Dynamics of Point-Vortex Data Assimilation

Dynamics of vortices and drift waves: a point vortex model

The complex interactions of localized vortices with waves is investigated using a model of point vortices in the presence of a transverse or longitudinal wave. This simple model shows a rich dynamical behavior including oscillations of a dipole, splitting and merging of two like-circulation vortices, and chaos. The analytical and numerical results of this model have been found to predict under ...